Simulations des micro-décharges de type MHCD

Transcription

1 Simulations ds micro-déchargs d typ MHCD Lann Pitchford Group GREPHE Laboratoir ds Plasmas t Convrsion d Enrgi Univrsité d Toulous t CNRS UMR 5213 pitchford@laplac.univ-tls.fr JP Bouf, G. Haglaar, Th Callgari Post-docs : E Munoz-Srrano, K. Makashva Étudiants : J. Lo, B. Eismann

2 MicroHollow Cathod Discharg Low voltag opration (~>200 V) Scaling to highr volums : - using arrays of MHCDs - 3-lctrod systms Plasma dnsitis up to cm -3 in air at atmosphric prssur cathod anod dilctric C A ~ 200 μm 200 μm

3 Modling/simulation : approach 1. Idntification of qustions 2. Dfinition of physical modl 3. Physical modl => numrical modl Goal: 4. Consistncy chcking, analytical tsts, snsitivity to input data,.convrgnc tsts,. (tim consuming part) 5. Gnration of numrical rsults 6. Intrprtation of rsults 7. Comparisons with xprimnt

4 Idntification of qustions - MHCD INPUT: gas composition, prssur, gomtry, cathod currnt, circuit RESULTS: E(x,t), n (x,t), n i (x,t), T g (x,t), spcis dnsitis From ths rsults, othr quantitis of intrst (currnt, currnt dnsity, filds at surfacs, ) can b dtrmind.

5 INPUT: MHCD - physical modl gas composition, prssur, gomtry, cathod currnt, circuit 2D cylindrical symmtry Chargd particl transport and gnration Variabls ar lctron dnsity, ion dnsity and potntial (or fild) Elctric Fild (Poisson s quation) + boundary conditions RESULTS: E(x,t), n (x,t), n i (x,t), T g (x,t), spcis dnsitis J.-P. Bœuf and L.C.Pitchford (1995) Phys.Rv.E, J.-P. Bœuf, L.C.Pitchford and K.H.Schonbach (2005) Appl.Phys.Ltt.

6 Elctron transport quations Continuity quation: n t Momntum balanc: (drift-diffusion approximation) n v +. n v = nν n ff μ E [ n D ] n v 3 f d v = n ν ff μ D = lctron flux = ffctiv ionization frquncy = lctron mobility = lctron diffusion cof.

7 Continuity Equation: n t +. n v = n ν ionization (rcombination) i rn n ( ) p 3 n ν = Nσ v f d v i i Elctron Vlocity Distribution Function: unknown ν i?

8 Elctron transport quations Continuity quation: n t n v +. n v = nν Momntum balanc: n Enrgy balanc: ff μ E (drift-diffusion approximation) [ n D ] n v 3 f d v = n ν ff μ D = lctron flux = ffctiv ionization frquncy = lctron mobility = lctron diffusion cof. n t ε 5 +. n ε v + q = - nv 3 E n v ε ε q v ε = lctron avg. nrgy = hat flux = nrgy xch. frq.

9 Hlium maxwllians Compar distribution functions for sam <> Maxwllian and from Boltzmann quation Boltzmann 5 V 10 V Maxwllian Boltzmann Compar rsulting ionization cofficnts (α/n, m 2 ) Avrag nrgy

10 Fluid modl Ion dnsity : Ion continuity Ion flux = drift + diffusion trms Elctron dnsity : Elctron continuity Elctron flux = drift + diffusion trms Elctron avrag nrgy Potntial : Poisson s quation Bœuf and Pitchford, PRE, (1995)

11 Scondary lctron mission : a boundary condition cathod j ion (cathod) j lctron (cathod) = γ ff j ion (cathod) γ ff = γ ion + γ photons + γ mtastabl W Mo Ar N from Fig in Collision Phnomna in Ionizd Gass, by E.W. McDanil, 1964

12 INPUT: MHCD - physical modl gas composition, prssur, gomtry, cathod currnt, circuit 2D cylindrical symmtry Chargd particl transport and gnration Excitd spcis kintics Elctric Fild (Poisson s quation) + boundary conditions Gas Tmpratur RESULTS: E(x,t), n (x,t), n i (x,t), T g (x,t), spcis dnsitis J.-P. Bœuf and L.C.Pitchford (1995) Phys.Rv.E, J.-P. Bœuf, L.C.Pitchford and K.H.Schonbach (2005) Appl.Phys.Ltt.

13 Equipotntial contours Without plasma : distribution of potntial dtrmind by th gomtry Axis of cylindrical symmtry C A dilctric

14 100 torr Xnon C A Equipotntial contours D = 240 microns Xmax = 0.1 cm Anod diamtr = 0.1 cm ma 10 contours from 0 to 243 V

15 100 torr Xnon Equipotntial contours C A C A C A Incrasing currnt Symmtry axis ma 0.13 ma 0.17 ma 10 contours from 0 to 243 V

16 100 torr Xnon Equipotntial contours C A C A C A Incrasing currnt Symmtry axis ma 0.13 ma 0.17 ma Sam scal all curvs, V, 10 contours

17 Plasma proprtis at 0.17 ma n X 2 + Xnon 100 torr Gas tmpratur x X M X cm cm Spcis numbr dnsitis (pak numbr dnsity cm -3 ) Tg pak = 450K Equipotntial contours

18 Comparison with xprimnt : MHCD Elctron numbr dnsity Expts : Sadghi and Lagrang lctron numbr dnsity (cm -3 ) 3x x10 14 Ar, 100 micron hol diamtr currnt (ma) modl xpt 1x torr 100 torr modl : on-axis pak dnsity 200 torr xpt : on-axis, viwd from anod sid

19 Gas tmpratur Expts : Sadghi and Lagrang Comparison with xprimnt : MHCD 700 Pak gas tmp (K) currnt (ma) modl 75 torr 100 torr 200 torr xpt 75 torr 100 torr 200 torr Modl rsults dpnd on assumptions rgarding accomodation cofficint and fractional ion powr dpositd in th gas. Prssur dpndnc diffrnt in modl and xprimnt. Modl rsults consistnt with Kushnr, 2005.

20 Calculatd V-I charactristics Xnon 100 torr Voltag (V) 280 γ only outsid γ only insid Currnt (ma) => Transition from low currnt "abnormal" glow discharg localizd insid th cathod hol to a highr currnt "normal" glow sprading along th outr cathod surfac. Th structur is not du to th classical hollow cathod ffct. Bœuf, Pitchford, and Schonbach, APL, 2005

21 MHCD V-I charactristic - X (xpt) MHCD 250 mbar, Xnon Voltag (V) currnt (ma) xprimntal rsults from B.J. L and K. Frank, Erlangn

22 MHCD V-I charactristic - X (xpt) Comparison with VUV mission intnsity mbar, Xnon 0.8 Voltag (V) voltag anod fac cathod fac VUV mission intnsity (a.u.) currnt (ma) xprimntal rsults from B.J. L and K. Frank, Erlangn

23 V-I charactristic - MHCD voltag (V) torr 300 torr 400 torr currnt (ma) Not ngativ slop, prssur dpndnc Argon, 200 micron hol diamtr X Aubrt and A Roussau,2007

24 CBL discharg lctrod gomtry Cathod, anod ~ molybdnum, 250 μm thick Dilctric ~ alumina, 250 μm thick Innr diamtr of th ring-shapd anod ~ 0.75 mm X, 1.5 mm Ar Schonbach t al., JAP 95, 4 (2004)

25 Voltag currnt charactristics: X DC mod opration Prssur ~ Torr Gas ~ X Abnormal glow mod (V I ) Slf-organization of th plasma Normal glow discharg (V = ct, I incrass) V prssur I transition α p Schonbach t al., JAP 95, 4 (2004)

26 Computational domain Dimnsions: DIELECTRIC Elctrods thicknss: 100 μm Dilctric thicknss: 500 μm Hol radius: 400 μm Domain: 2.4 x 1.6 mm Cylindrical coordinat systm axially symmtric ANODE Non-uniform grid: 120 x 80 nods CATHODE

27 Ar, 100 Torr, (1.31 ma, 206 V) 1.2 Potntial (V) 1.2 Gas tmpratur (K) 1.2 Ar* numbr dnsity (cm -3 ) R (cm) z (cm) R (cm) T max = K z (cm) R (cm) n Ar* max =2.77E14 cm z (cm) 2.8E1 1E14 3.9E1 1.5E1 5.4E1 2E12 7.5E1 2.8E1 1.2 Elctron numbr dnsity (cm -3 ) 1.2 Ar + numbr dnsity (cm -3 ) 1.2 Ar 2 + numbr dnsity (cm -3 ) R (cm) n max =6.65E13 cm -3 7E13 3.6E1 1.9E1 9.7E1 R (cm) 5E12 2.6E1 1.4E1 7E n Ar+ max =5.58E13 cm -3 6E11 1.2E1 2.2E1 4.3E1 R (cm) 8.3E1 1.6E1 3.1E1 6E n Ar2+ max =1.28E13 cm E1 2.7E1 5.2E1 1E12 1.9E1 3.8E1 7.3E1 1.4E z (cm) z (cm) z (cm)

28 R (cm) R (cm) Dirct ionization Sourc Trm (cm -3 s -1 ) z (cm) Stpwis ionization Sourc Trm (cm -3 s -1 ) z (cm) 1E20 3E19 1E19 3E18 1E18 3E17 1E17 3E16 1E16 3E15 1E15 4E20 1E20 3E19 8E18 2E18 6E17 2E17 5E16 1E16 4E15 1E15 R (cm) r (cm) z (cm) Dissociativ Rcombination Sourc Trm (cm -3 s -1 ) z (cm) 5E19 2E19 5E18 2E18 6E17 2E17 7E16 2E16 9E15 3E15 1E15 R (cm) Total Elctron Sourc Trm (cm -3 s -1 ) Stotal< z (cm) 5E20 1E20 3E19 9E18 2E18 7E17 2E17 5E16 1E16 4E15 1E15

29 V-I curv Voltag (V) Argon, 100 Torr factor=0.25 factor=1.0 E Currnt (ma) F Maximum Tmpratur (K) Argon, 100 Torr factor=0.25 factor= Currnt (ma) Factor 1 Economou, Plasma Sourcs Sci. Tchnol. 17 (2008)

30 Excimr powr Powr Excimr Powr (mw) f( r, z) K xc( r, z) n( r, z) nar( r, z) dv = = ε f( r, z) Sxc( r, z) ε dv f( r, z) = S S Argon p = 100 torr p = 400 torr 3 body Ar2* Ar* total loss 1 10 Currnt (ma) Critrion for th transition point Schonbach t al., JAP 95, 4 (2004)

31 Incrasing currnt Mtastabl Powr (mw) Excimr Powr (mw) Currnt (ma) Argon p = 400 torr Argon p = 400 torr Abnormal glow Normal glow Voltag (V) A Argon p = 100 torr p = 400 torr B C D Currnt (ma) Currnt (ma) CATHODE BOUNDARY LAYER DISCHARGE (CBL)

32 Excimr fficincy Efficincy(%) = Excimr Powr 100 V I Excimr Efficincy (%) Argon p = 100 torr p = 400 torr Currnt (ma) Schonbach t al., JAP 95, 4 (2004) 32 CATHODE BOUNDARY LAYER DISCHARGE (CBL) 27/11/2009

33 Influnc of th dilctric thicknss D = 300 μm Voltag (V) D = 250 μm D = 200 μm D = 150 μm D = 130 μm p = 200 Torr d = 200 μm C = 100 μm; A = 100 μm Currnt (ma) Argon, 100 torr Makashva t al, ICPIG 2008

34 2-hols Ar, 100 Torr, (13.4 ma, 200 V) 34 CATHODE BOUNDARY LAYER DISCHARGE (CBL) 27/11/2009

35 O 2 ( 1 Δ) gnration in microplasmas O 2 ( 1 Δ) : mtastabl oxygn molcul, 0.98 V % lctrical nrgy into O 2 ( 1 Δ) % 100% O 2 20% 5% E/N (Td) % lctrical nrgy into O 2 ( 1 Δ) % 20 % 50 % 100 % O E/N (Td) H/O 2 mixturs Ar/O 2 mixturs

36 Cold cathod, glow dischargs Elctrons mittd from th cathod du to ion bombardmnt Elctron-ion pairs cratd in volum ionization vnts Φ+ Φ - Cathod (V=0) plasma Anod (V=+V) dnsitis (cm -3 ) Elctric fild (kv/cm) x x x ,0 0,5 1,0 1,5 2,0 distanc (cm)

37 Hollow Cathod Discharg plasma potntial bulk lctrons bouncing lctrons cathod cathod anod bulk lctrons can b dscribd by a fluid modl "pndulum" lctrons cannot

38 Glow dischargs & non-thrmal plasmas Schmatic V-I charactristic Glow Discharg: ~ 1-10 torr cm ~ V ~ μa/cm 2 -ma/cm 2 Voltag Log Currnt Non-thrmal Plasma: Ionization dgr < Elctron man nrgy ~1-10 V T >> Ion & gas tmpratur

39 Structur of a glow discharg V j + j = γ j + plasma... Rgion: Shath Glow Positiv column Elctric High Vry low Fild dtrmind by fild: ionization balanc Powr Ions-> Elctron bam Elctron bulk dposition: gas/cathod ->ionization, hating xcitation, dissoc.

40 Scondary lctron yild dtrmind from brakdown data Phlps, and Ptrovic, Plasma Sci Sourcs & Tch, vol 8, 1999, p. B1 Effctiv lctron scondary lctron mission cofficint vs E/N(cathod) Masurd and calculatd V-j/p 2 In argon glow dischargs